8279:
4308:
3638:
5702:(relative to the mass contained in the sphere of matter closer to the origin) is equal to a constant related to the curvature of the universe. In other words, the energy (relative to the origin) of a co-moving particle in free-fall is conserved. General relativity merely adds a connection between the spatial curvature of the universe and the energy of such a particle: positive total energy implies negative curvature and negative total energy implies positive curvature.
8255:
4321:
570:
47:
1217:
8315:
8339:
8291:
582:
8327:
8303:
6071:
dipole through studies of radio galaxies and quasars show disagreement in the magnitude. Taken at face value, these observations are at odds with the
Universe being described by the FLRW metric. Moreover, one can argue that there is a maximum value to the Hubble constant within an FLRW cosmology tolerated by current observations,
1031:
1745:
4812:
model. Because the FLRW model assumes homogeneity, some popular accounts mistakenly assert that the Big Bang model cannot account for the observed lumpiness of the universe. In a strictly FLRW model, there are no clusters of galaxies or stars, since these are objects much denser than a typical part
6070:
and its generalization, astrophysicists now agree that the early universe is almost homogeneous and isotropic (when averaged over a very large scale) and thus nearly a FLRW spacetime. That being said, attempts to confirm the purely kinematic interpretation of the Cosmic
Microwave Background (CMB)
5785:
from the UK explored the problem further during the 1930s. In 1935 Robertson and Walker rigorously proved that the FLRW metric is the only one on a spacetime that is spatially homogeneous and isotropic (as noted above, this is a geometric result and is not tied specifically to the equations of
4813:
of the universe. Nonetheless, the FLRW model is used as a first approximation for the evolution of the real, lumpy universe because it is simple to calculate, and models that calculate the lumpiness in the universe are added onto the FLRW models as extensions. Most cosmologists agree that the
2130:
3616:
4653:
4799:
5056:
1505:
935:
2732:
2889:
1212:{\displaystyle \mathrm {d} \mathbf {\Sigma } ^{2}={\frac {\mathrm {d} r^{2}}{1-kr^{2}}}+r^{2}\mathrm {d} \mathbf {\Omega } ^{2},\quad {\text{where }}\mathrm {d} \mathbf {\Omega } ^{2}=\mathrm {d} \theta ^{2}+\sin ^{2}\theta \,\mathrm {d} \phi ^{2}.}
2358:
5682:
3427:
1380:
A disadvantage of reduced circumference coordinates is that they cover only half of the 3-sphere in the case of positive curvature—circumferences beyond that point begin to decrease, leading to degeneracy. (This is not a problem if space is
5563:
1543:
4930:
3115:
3260:
6044:
or anisotropic? Is the CMB dipole purely kinematic, or does it signal a possible breakdown of the FLRW metric? Even if the cosmological principle is correct, is the
Friedmann–Lemaître–Robertson–Walker metric valid in the late
5691:) is the amount that leaves through the sides due to the expansion of the universe plus the mass equivalent of the work done by pressure against the material being expelled. This is the conservation of mass–energy (
5208:
3709:
5746:, acted as the scientific referee of Friedmann's work. Eventually Einstein acknowledged the correctness of Friedmann's calculations, but failed to appreciate the physical significance of Friedmann's predictions.
4508:
1929:
3438:
4524:
2213:
5251:
4659:
4936:
4371:
Einstein's field equations are not used in deriving the general form for the metric: it follows from the geometric properties of homogeneity and isotropy. However, determining the time evolution of
5942:
2959:
5424:
1821:
1535:
1320:
999:
2506:
1411:
2456:
6872:
Abdalla, Elcio; et al. (June 2022). "Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies".
5879:
820:
4825:. As of 2003, the theoretical implications of the various extensions to the FLRW model appear to be well understood, and the goal is to make these consistent with observations from
2570:
6106:, and depending on how local determinations converge, this may point to a breakdown of the FLRW metric in the late universe, necessitating an explanation beyond the FLRW metric.
2743:
2410:
960:
4352:
5304:
2272:
5569:
3266:
5356:
7108:. The original work is Ehlers, J., Geren, P., Sachs, R.K.: Isotropic solutions of Einstein-Liouville equations. J. Math. Phys. 9, 1344 (1968). For the generalization, see
542:
2244:
6616:
5771:
5126:
4430:
8359:
3731:
1740:{\displaystyle S_{k}(r)={\begin{cases}{\sqrt {k}}^{\,-1}\sin(r{\sqrt {k}}),&k>0\\r,&k=0\\{\sqrt {|k|}}^{\,-1}\sinh(r{\sqrt {|k|}}),&k<0.\end{cases}}}
7025:
Krishnan, Chethan; Mohayaee, Roya; Colgáin, Eoin Ó; Sheikh-Jabbari, M. M.; Yin, Lu (16 September 2021). "Does Hubble
Tension Signal a Breakdown in FLRW Cosmology?".
5447:
6096:
6009:
2558:
4398:
8364:
6831:
2899:
In more general FLRW space using spherical coordinates (called "reduced-circumference polar coordinates" above), the surviving components of the Ricci tensor are
5754:
4847:
2965:
6614:(1931), "Expansion of the universe, A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic nebulæ",
5985:
5965:
5079:
3936:
3121:
8005:
7264:
Krishnan, Chethan; Mohayaee, Roya; Ó Colgáin, Eoin; Sheikh-Jabbari, M. M.; Yin, Lu (2021-05-25). "Does Hubble tension signal a breakdown in FLRW cosmology?".
738:. The general form of the metric follows from the geometric properties of homogeneity and isotropy; Einstein's field equations are only needed to derive the
612:
8240:
8029:
7775:
5441:
This is due to McCrea and Milne, although sometimes incorrectly ascribed to
Friedmann. The Friedmann equations are equivalent to this pair of equations:
4289:
4099:
3941:
4054:
4345:
7092:
5698:
The second equation says that the kinetic energy (seen from the origin) of a particle of unit mass moving with the expansion plus its (negative)
7811:
7765:
3967:
3801:
8278:
6650:(1927), "Un univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques",
4307:
2125:{\displaystyle S_{k}(r)=\sum _{n=0}^{\infty }{\frac {(-1)^{n}k^{n}r^{2n+1}}{(2n+1)!}}=r-{\frac {kr^{3}}{6}}+{\frac {k^{2}r^{5}}{120}}-\cdots }
7949:
7398:
7332:
7102:
6320:
6295:
6270:
6245:
6040:
and assumed by all models that use the
Friedmann–Lemaître–Robertson–Walker metric, including the current version of ΛCDM, or is the universe
5162:
4006:
3644:
703:
3611:{\displaystyle R={\frac {6}{c^{2}}}\left({\frac {{\ddot {a}}(t)}{a(t)}}+{\frac {{\dot {a}}^{2}(t)}{a^{2}(t)}}+{\frac {k}{a^{2}(t)}}\right).}
814:
of space. It also assumes that the spatial component of the metric can be time-dependent. The generic metric that meets these conditions is
7433:
6059:
6048:
4445:
346:
6067:
5761:(Annals of the Scientific Society of Brussels). In the face of the observational evidence for the expansion of the universe obtained by
4648:{\displaystyle \left({\frac {\dot {a}}{a}}\right)^{2}+{\frac {kc^{2}}{a^{2}}}-{\frac {\Lambda c^{2}}{3}}={\frac {\kappa c^{4}}{3}}\rho }
4338:
8057:
7686:
6218:
3718:
7152:
Siewert, Thilo M.; Schmidt-Rubart, Matthias; Schwarz, Dominik J. (2021). "Cosmic radio dipole: Estimators and frequency dependence".
5260:
can be interpreted as arising from a form of energy that has negative pressure, equal in magnitude to its (positive) energy density:
974:. It is normally written as a function of three spatial coordinates, but there are several conventions for doing so, detailed below.
7691:
5817:
4794:{\displaystyle 2{\frac {\ddot {a}}{a}}+\left({\frac {\dot {a}}{a}}\right)^{2}+{\frac {kc^{2}}{a^{2}}}-\Lambda c^{2}=-\kappa c^{2}p.}
3744:
1365:
555:
8011:
6240:. Springer Praxis books in astronomy and planetary science (2. ed., reprinted ed.). Chichester, UK: Praxis Publ. p. 61.
5051:{\displaystyle {\frac {\ddot {a}}{a}}=-{\frac {\kappa c^{4}}{6}}\left(\rho +{\frac {3p}{c^{2}}}\right)+{\frac {\Lambda c^{2}}{3}}}
4024:
2141:
5214:
3637:
605:
7724:
6422:
Rosu, Haret C.; Mancas, S. C.; Chen, Pisin (2015-05-05). "Barotropic FRW cosmologies with
Chiellini damping in comoving time".
3931:
188:
7827:
5805:) that assume that the only contributions to stress–energy are cold matter ("dust"), radiation, and a cosmological constant.
742:
of the universe as a function of time. Depending on geographical or historical preferences, the set of the four scientists –
550:
264:
7905:
7968:
7205:
Secrest, Nathan J.; Hausegger, Sebastian von; Rameez, Mohamed; Mohayaee, Roya; Sarkar, Subir; Colin, Jacques (2021-02-25).
5890:
4064:
8258:
8000:
7835:
4433:
4018:
3726:
193:
116:
6336:
4084:
7822:
6126:
multiple connectedness in the positive curvature case and says that "we are still free to restore" simple connectedness.
7582:
5738:
published his work, it remained relatively unnoticed by his contemporaries. Friedmann was in direct communication with
8369:
7863:
7597:
7111:
7088:
5692:
5089:
4325:
3816:
3736:
2905:
598:
574:
121:
4515:
1500:{\displaystyle \mathrm {d} \mathbf {\Sigma } ^{2}=\mathrm {d} r^{2}+S_{k}(r)^{2}\,\mathrm {d} \mathbf {\Omega } ^{2}}
5378:
1799:
1513:
1298:
977:
8269:
8150:
7592:
7545:
4826:
4229:
3777:
340:
320:
128:
73:
5099:
The second equation states that both the energy density and the pressure cause the expansion rate of the universe
4029:
2463:
8180:
7806:
7487:
6926:
6191:
Ellis, G. F. R.; van Elst, H. (1999). "Cosmological models (Cargèse lectures 1998)". In Marc Lachièze-Rey (ed.).
5734:
3841:
2416:
1284:
930:{\displaystyle -c^{2}\mathrm {d} \tau ^{2}=-c^{2}\mathrm {d} t^{2}+{a(t)}^{2}\mathrm {d} \mathbf {\Sigma } ^{2},}
723:
166:
4104:
8205:
7755:
7515:
7426:
4440:
4264:
4254:
3921:
2727:{\displaystyle R_{tt}=-3{\frac {\ddot {a}}{a}},\quad R_{xx}=R_{yy}=R_{zz}=c^{-2}(a{\ddot {a}}+2{\dot {a}}^{2})}
1014:
739:
707:
335:
100:
7934:
7856:
5834:
5368:
In fact, in order to get a term that causes an acceleration of the universe expansion, it is enough to have a
3983:
1834:
may be taken to belong to the set {−1 ,0, +1} (for negative, zero, and positive curvature respectively). Then
8374:
7476:
7467:
6041:
5732:
first derived the main results of the FLRW model in 1922 and 1924. Although the prestigious physics journal
5082:
4822:
4249:
303:
183:
8023:
7929:
6953:
Migkas, K.; Schellenberger, G.; Reiprich, T. H.; Pacaud, F.; Ramos-Ceja, M. E.; Lovisari, L. (April 2020).
5687:
The first equation says that the decrease in the mass contained in a fixed cube (whose side is momentarily
5132:, with pressure playing a similar role to that of energy (or mass) density, according to the principles of
4049:
2884:{\displaystyle R=6c^{-2}\left({\frac {{\ddot {a}}(t)}{a(t)}}+{\frac {{\dot {a}}^{2}(t)}{a^{2}(t)}}\right).}
8160:
7887:
7561:
7525:
6826:
6037:
5988:
5821:
5782:
5430:
4219:
4204:
3811:
755:
735:
6011:
is the density of space of this universe. The numerical value of
Einstein's radius is of the order of 10
2353:{\displaystyle \mathrm {d} \mathbf {\Sigma } ^{2}=\mathrm {d} x^{2}+\mathrm {d} y^{2}+\mathrm {d} z^{2}.}
8165:
7770:
7709:
6790:
6749:
6710:
6024:
5706:
5677:{\displaystyle {\frac {{\dot {a}}^{2}}{2}}-{\frac {\kappa c^{4}a^{3}\rho }{6a}}=-{\frac {kc^{2}}{2}}\,.}
5257:
5153:
5137:
5128:
to decrease, i.e., both cause a deceleration in the expansion of the universe. This is a consequence of
4194:
3762:
3422:{\displaystyle R_{\phi \phi }=r^{2}(c^{-2}(a(t){\ddot {a}}(t)+2{\dot {a}}^{2}(t))+2k)\sin ^{2}(\theta )}
2376:
943:
807:
715:
508:
310:
252:
5266:
8070:
7996:
7840:
7442:
7355:
7283:
7228:
7171:
7123:
7044:
6976:
6955:"Probing cosmic isotropy with a new X-ray galaxy cluster sample through the L X – T scaling relation"
6891:
6840:
6799:
6758:
6719:
6688:
6659:
6625:
6576:
6530:
6492:
6441:
6379:
6206:
6157:
5699:
4014:
521:
493:
315:
5884:
in the
Friedmann equation, the radius of curvature of space of this universe (Einstein's radius) is
5088:
The first equation can be derived also from thermodynamical considerations and is equivalent to the
1574:
8343:
8145:
8140:
8135:
8130:
7962:
7911:
7729:
7714:
7540:
7471:
7419:
6931:
6785:
6744:
6705:
6676:
6647:
6611:
6564:
6518:
6063:
5778:
5750:
5729:
5369:
5322:
5096:(which is implicitly assumed in the derivation of the Friedmann–Lemaître–Robertson–Walker metric).
4814:
4511:
4366:
4209:
4189:
4179:
4174:
4159:
3926:
1862:
1382:
751:
747:
743:
453:
413:
383:
330:
286:
274:
178:
68:
8034:
5709:
term is assumed to be treated as dark energy and thus merged into the density and pressure terms.
4069:
8331:
8319:
8210:
8110:
7892:
7873:
7867:
7818:
7760:
7669:
7587:
7505:
7482:
7450:
7299:
7273:
7246:
7218:
7187:
7161:
7068:
7034:
7000:
6966:
6907:
6881:
6592:
6546:
6465:
6431:
6403:
6369:
6196:
6173:
6147:
5362:
5133:
4259:
4144:
3916:
3821:
3806:
3767:
3629:
2225:
1774:
1249:
791:
711:
534:
473:
443:
408:
378:
325:
269:
38:
5102:
5793:
since they proved its generic properties, is different from the dynamical "Friedmann–Lemaître"
5558:{\displaystyle -a^{3}{\dot {\rho }}=3a^{2}{\dot {a}}\rho +{\frac {3a^{2}p{\dot {a}}}{c^{2}}}\,}
4403:
8220:
8090:
8052:
8044:
7645:
7602:
7394:
7373:
7328:
7098:
7060:
6992:
6457:
6395:
6316:
6291:
6266:
6241:
6214:
5717:
5093:
4139:
4089:
3864:
1909:
1824:
1323:
1225:
is a constant representing the curvature of the space. There are two common unit conventions:
699:
503:
6235:
8295:
8185:
8125:
8115:
8062:
8039:
7617:
7363:
7291:
7236:
7179:
7175:
7131:
7114:(2007), "Proving Almost-Homogeneity of the Universe: An Almost Ehlers-Geren-Sachs Theorem",
7052:
6984:
6980:
6899:
6848:
6807:
6766:
6727:
6633:
6584:
6538:
6500:
6449:
6387:
6165:
6055:
5825:
5766:
4809:
4234:
4214:
4169:
4149:
4094:
971:
963:
795:
636:
586:
398:
388:
373:
224:
93:
6074:
5994:
5757:, arrived independently at results similar to those of Friedmann and published them in the
4925:{\displaystyle {\dot {\rho }}=-3{\frac {\dot {a}}{a}}\left(\rho +{\frac {p}{c^{2}}}\right)}
3110:{\displaystyle R_{rr}={\frac {c^{-2}(a(t){\ddot {a}}(t)+2{\dot {a}}^{2}(t))+2k}{1-kr^{2}}}}
2531:
8200:
8175:
8100:
8095:
7978:
7939:
7901:
7845:
7719:
7655:
7393:(Repr ed.). Oxford : New York: Clarendon Press ; Oxford University Press.
6138:
5739:
4374:
4269:
4244:
4129:
4124:
3988:
3869:
3831:
3255:{\displaystyle R_{\theta \theta }=r^{2}(c^{-2}(a(t){\ddot {a}}(t)+2{\dot {a}}^{2}(t))+2k)}
967:
798:. The FLRW model was developed independently by the named authors in the 1920s and 1930s.
513:
448:
433:
418:
403:
393:
257:
7983:
4039:
154:
7359:
7287:
7232:
7127:
7048:
6895:
6844:
6803:
6762:
6723:
6692:
6663:
6629:
6580:
6567:(1924). "Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes".
6534:
6496:
6445:
6383:
6210:
6161:
6058:, uses the FLRW metric. By combining the observation data from some experiments such as
4400:
does require
Einstein's field equations together with a way of calculating the density,
8283:
8225:
7897:
7881:
7877:
7780:
7750:
7607:
7510:
7387:
6360:
Rosu, H. C.; Ojeda-May, P. (June 2006). "Supersymmetry of FRW Barotropic Cosmologies".
5970:
5950:
5064:
4312:
4279:
4274:
3962:
3826:
731:
498:
458:
17:
7407:(See Chapter 23 for a particularly clear and concise introduction to the FLRW models.)
6483:
McCrea, W. H.; Milne, E. A. (1934). "Newtonian universes and the curvature of space".
27:
Metric based on the exact solution of Einstein's field equations of general relativity
8353:
8215:
8195:
8190:
8105:
7973:
7801:
7745:
7577:
7530:
7303:
7250:
7191:
7072:
7004:
6911:
6596:
6550:
6407:
6177:
6169:
4239:
4199:
4154:
4134:
4059:
3957:
3836:
2219:
1268:
483:
468:
368:
6954:
6469:
6036:
Is the universe homogeneous and isotropic at large enough scales, as claimed by the
8307:
8235:
8155:
8120:
7650:
7612:
5769:, and in 1930–31 Lemaître's paper was translated into English and published in the
5762:
5713:
4841:
The pair of equations given above is equivalent to the following pair of equations
4518:
is similarly assumed to be isotropic and homogeneous. The resulting equations are:
4184:
4164:
2561:
1921:
488:
463:
438:
423:
279:
7183:
6988:
7322:
8019:
7988:
7535:
6903:
5310:
5141:
5129:
4074:
4044:
1271:
because it is equal to the measured circumference of a circle (at that value of
236:
229:
7295:
7241:
7206:
7056:
8230:
7796:
7640:
7635:
6852:
6504:
6453:
6391:
6343:
6012:
4284:
3846:
3772:
478:
7377:
7368:
7343:
7064:
6996:
6638:
6461:
6399:
7627:
3855:
794:, although such a description is also associated with the further developed
719:
428:
1025:
In reduced-circumference polar coordinates the spatial metric has the form
5786:
general relativity, which were always assumed by Friedmann and Lemaître).
8170:
7520:
4805:
4224:
4034:
3874:
811:
727:
161:
63:
56:
5753:, a Belgian priest, astronomer and periodic professor of physics at the
2560:
FLRW space using Cartesian coordinates, the surviving components of the
6601:
English trans. in 'General Relativity and Gravitation' 1999 vol.31, 31–
6588:
6542:
5828:
that was supposed to represent our universe in idealized form. Putting
5203:{\displaystyle \rho \rightarrow \rho -{\frac {\Lambda }{\kappa c^{2}}}}
3704:{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}
6374:
6201:
6152:
1796:) is often chosen to equal 1 in the present cosmological era, so that
1295:) is often chosen to equal 1 in the present cosmological era, so that
46:
7850:
6886:
5720:
effects. So they may cause a deviation from the Friedmann equations.
4503:{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu }}
5765:
in the late 1920s, Lemaître's results were noticed in particular by
8302:
7278:
7223:
7166:
7136:
7039:
6971:
6812:
6771:
6731:
6436:
6028:
2515:
is one of the radial coordinates defined above, but this is rare.
962:
ranges over a 3-dimensional space of uniform curvature, that is,
7831:
4830:
1337:(for negative, zero, and positive curvature respectively). Then
7415:
648:
7411:
6288:
Spacetime and geometry: an introduction to general relativity
6136:
Lachieze-Rey, M.; Luminet, J.-P. (1995). "Cosmic Topology".
2208:{\displaystyle S_{k}(r)=r\;\mathrm {sinc} \,(r{\sqrt {k}}),}
5246:{\displaystyle p\rightarrow p+{\frac {\Lambda }{\kappa }}.}
1733:
686:
677:
668:
657:
7324:
The measure of the universe: a history of modern cosmology
6290:. New York: Cambridge University Press. pp. 329–333.
5156:
term can be omitted if we make the following replacements
6195:. NATO Science Series C. Vol. 541. pp. 1–116.
6122:
For an early reference, see Robertson (1935); Robertson
4821:, i.e., a model that follows the FLRW metric apart from
2246:
is one of the imaginary, zero or real square roots of
8267:
6265:. Chicago: University of Chicago Press. p. 116.
6077:
5997:
5973:
5953:
5937:{\displaystyle R_{\text{E}}=c/{\sqrt {4\pi G\rho }},}
5893:
5837:
5572:
5450:
5381:
5325:
5269:
5217:
5165:
5105:
5067:
4939:
4850:
4662:
4527:
4448:
4406:
4377:
3647:
3441:
3269:
3124:
2968:
2908:
2746:
2573:
2534:
2466:
2419:
2379:
2275:
2228:
2144:
1932:
1802:
1546:
1516:
1414:
1301:
1034:
980:
946:
823:
660:
642:
6315:. Chicago: University of Chicago Press. p. 97.
1757:
may be taken to have units of length, in which case
1385:, i.e. a 3-sphere with opposite points identified.)
1232:
may be taken to have units of length, in which case
683:
680:
665:
651:
645:
8083:
7948:
7920:
7789:
7738:
7700:
7679:
7668:
7626:
7570:
7554:
7496:
7460:
7449:
7207:"A Test of the Cosmological Principle with Quasars"
7150:See Siewert et al. for a recent summary of results
674:
671:
654:
639:
7386:
6090:
6003:
5979:
5959:
5936:
5873:
5676:
5557:
5418:
5350:
5298:
5245:
5202:
5120:
5073:
5050:
4924:
4793:
4647:
4502:
4424:
4392:
3703:
3610:
3421:
3254:
3109:
2953:
2883:
2726:
2552:
2500:
2450:
2404:
2352:
2238:
2207:
2124:
1815:
1750:As before, there are two common unit conventions:
1739:
1529:
1499:
1314:
1211:
993:
954:
929:
7348:Monthly Notices of the Royal Astronomical Society
6617:Monthly Notices of the Royal Astronomical Society
5789:This solution, often called the Robertson–Walker
5772:Monthly Notices of the Royal Astronomical Society
1904:Though it is usually defined piecewise as above,
6829:(1937), "On Milne's theory of world-structure",
2954:{\displaystyle R_{tt}=-3{\frac {\ddot {a}}{a}},}
1005:– all of the time dependence is in the function
7344:"Classification of Uniform Cosmological Models"
6681:Annales de la Société Scientifique de Bruxelles
6652:Annales de la Société Scientifique de Bruxelles
5759:Annales de la Société Scientifique de Bruxelles
5092:, assuming the expansion of the universe is an
1405:is proportional to radial distance; this gives
6832:Proceedings of the London Mathematical Society
6788:(1936), "Kinematics and world structure III",
5419:{\displaystyle p<-{\frac {\rho c^{2}}{3}}.}
4804:These equations are the basis of the standard
1816:{\displaystyle \mathrm {d} \mathbf {\Sigma } }
1530:{\displaystyle \mathrm {d} \mathbf {\Omega } }
1315:{\displaystyle \mathrm {d} \mathbf {\Sigma } }
994:{\displaystyle \mathrm {d} \mathbf {\Sigma } }
806:The FLRW metric starts with the assumption of
7427:
6867:
6865:
6863:
6861:
6747:(1936), "Kinematics and world structure II",
6054:The current standard model of cosmology, the
5309:which is an equation of state of vacuum with
4346:
606:
8:
6362:International Journal of Theoretical Physics
5081:, the spatial curvature index, serving as a
2501:{\displaystyle z=r\sin \theta \sin \phi \,,}
5695:) contained within a part of the universe.
2451:{\displaystyle y=r\sin \theta \cos \phi \,}
2250:. These definitions are valid for all
7676:
7457:
7434:
7420:
7412:
6708:(1935), "Kinematics and world structure",
4353:
4339:
3905:
3795:
3625:
2170:
627:Friedmann–Lemaître–Robertson–Walker metric
613:
599:
213:
87:
45:
29:
7367:
7277:
7240:
7222:
7165:
7135:
7038:
6970:
6885:
6811:
6770:
6637:
6435:
6373:
6200:
6151:
6082:
6076:
5996:
5972:
5952:
5915:
5910:
5898:
5892:
5854:
5853:
5839:
5838:
5836:
5670:
5658:
5648:
5622:
5612:
5602:
5588:
5577:
5576:
5573:
5571:
5554:
5546:
5530:
5529:
5520:
5510:
5493:
5492:
5486:
5465:
5464:
5458:
5449:
5401:
5391:
5380:
5342:
5324:
5292:
5286:
5268:
5230:
5216:
5191:
5178:
5164:
5107:
5106:
5104:
5066:
5036:
5026:
5010:
4996:
4973:
4963:
4942:
4940:
4938:
4909:
4900:
4874:
4872:
4852:
4851:
4849:
4808:cosmological model including the current
4779:
4760:
4742:
4731:
4721:
4712:
4693:
4691:
4668:
4666:
4661:
4630:
4620:
4605:
4595:
4584:
4573:
4563:
4554:
4535:
4533:
4526:
4491:
4472:
4453:
4447:
4405:
4376:
3692:
3683:
3671:
3652:
3646:
3582:
3572:
3551:
3530:
3519:
3518:
3514:
3474:
3473:
3470:
3457:
3448:
3440:
3401:
3367:
3356:
3355:
3328:
3327:
3303:
3290:
3274:
3268:
3222:
3211:
3210:
3183:
3182:
3158:
3145:
3129:
3123:
3098:
3056:
3045:
3044:
3017:
3016:
2992:
2985:
2973:
2967:
2933:
2931:
2913:
2907:
2855:
2834:
2823:
2822:
2818:
2778:
2777:
2774:
2760:
2745:
2715:
2704:
2703:
2685:
2684:
2669:
2653:
2637:
2621:
2598:
2596:
2578:
2572:
2533:
2494:
2465:
2447:
2418:
2398:
2378:
2341:
2332:
2323:
2314:
2305:
2296:
2287:
2282:
2276:
2274:
2229:
2227:
2192:
2185:
2171:
2149:
2143:
2104:
2094:
2087:
2072:
2062:
2012:
2002:
1992:
1976:
1970:
1959:
1937:
1931:
1808:
1803:
1801:
1706:
1698:
1696:
1675:
1674:
1667:
1659:
1657:
1607:
1586:
1585:
1578:
1569:
1551:
1545:
1522:
1517:
1515:
1491:
1486:
1480:
1479:
1473:
1457:
1444:
1435:
1426:
1421:
1415:
1413:
1307:
1302:
1300:
1200:
1191:
1190:
1178:
1165:
1156:
1147:
1142:
1136:
1131:
1121:
1116:
1110:
1104:
1088:
1067:
1058:
1055:
1046:
1041:
1035:
1033:
986:
981:
979:
947:
945:
918:
913:
907:
901:
887:
877:
868:
862:
846:
837:
831:
822:
6521:(1922). "Über die Krümmung des Raumes".
5874:{\displaystyle {\dot {a}}={\ddot {a}}=0}
4439:This metric has an analytic solution to
1884:is essentially a third angle along with
8360:Coordinate charts in general relativity
8274:
7094:The large scale structure of space-time
6234:Bergström, Lars; Goobar, Ariel (2008).
6193:Theoretical and Observational Cosmology
6115:
5142:causes an acceleration in the expansion
3975:
3949:
3908:
3854:
3628:
1275:), centered at the origin, divided by 2
1021:Reduced-circumference polar coordinates
244:
216:
108:
37:
5808:
1865:of the space, and may also be written
1368:of the space, and may also be written
786:). This model is sometimes called the
8365:Exact solutions in general relativity
7:
6927:"Do We Live in a Lopsided Universe?"
8006:Tolman–Oppenheimer–Volkoff equation
7959:Friedmann–Lemaître–Robertson–Walker
6874:Journal of High Energy Astrophysics
6237:Cosmology and particle astrophysics
6049:(more unsolved problems in physics)
5797:, which are specific solutions for
6679:(1933), "l'Univers en expansion",
5232:
5180:
5029:
4753:
4598:
4465:
3664:
2405:{\displaystyle x=r\cos \theta \,,}
2333:
2315:
2297:
2277:
2181:
2178:
2175:
2172:
1971:
1804:
1518:
1481:
1436:
1416:
1333:may be taken to belong to the set
1303:
1192:
1157:
1137:
1111:
1059:
1036:
982:
955:{\displaystyle \mathbf {\Sigma } }
908:
869:
838:
341:2dF Galaxy Redshift Survey ("2dF")
25:
7776:Hamilton–Jacobi–Einstein equation
7389:Introducing Einstein's relativity
5989:Newtonian constant of gravitation
5814:Einstein's radius of the universe
5809:Einstein's radius of the universe
5749:Friedmann died in 1925. In 1927,
5429:Such a field is sometimes called
5316:An attempt to generalize this to
556:Timeline of cosmological theories
321:Cosmic Background Explorer (COBE)
8337:
8325:
8313:
8301:
8289:
8277:
8254:
8253:
7327:. New York: Dover Publications.
6925:Billings, Lee (April 15, 2020).
6485:Quarterly Journal of Mathematics
6420:Their solutions can be found in
5299:{\displaystyle p=-\rho c^{2}\,,}
4320:
4319:
4306:
3636:
2283:
1809:
1523:
1487:
1422:
1308:
1267:is sometimes called the reduced
1143:
1117:
1042:
987:
948:
914:
635:
580:
569:
568:
4823:primordial density fluctuations
2616:
2218:where sinc is the unnormalized
1130:
336:Sloan Digital Sky Survey (SDSS)
189:Future of an expanding universe
7583:Mass–energy equivalence (E=mc)
7097:, Cambridge University Press,
5700:gravitational potential energy
5365:without further modification.
5221:
5169:
4434:cosmological equation of state
4416:
4410:
4387:
4381:
3594:
3588:
3563:
3557:
3542:
3536:
3505:
3499:
3491:
3485:
3416:
3410:
3394:
3382:
3379:
3373:
3345:
3339:
3324:
3318:
3312:
3296:
3249:
3237:
3234:
3228:
3200:
3194:
3179:
3173:
3167:
3151:
3071:
3068:
3062:
3034:
3028:
3013:
3007:
3001:
2867:
2861:
2846:
2840:
2809:
2803:
2795:
2789:
2721:
2678:
2547:
2535:
2199:
2186:
2161:
2155:
2044:
2029:
1989:
1979:
1949:
1943:
1920:. It can also be written as a
1777:of the space at the time when
1713:
1707:
1699:
1690:
1668:
1660:
1614:
1601:
1563:
1557:
1470:
1463:
1252:of the space at the time when
897:
891:
551:History of the Big Bang theory
347:Wilkinson Microwave Anisotropy
1:
7266:Classical and Quantum Gravity
7110:Stoeger, W. R.; Maartens, R;
7027:Classical and Quantum Gravity
6015:, or 10 billion light years.
5755:Catholic University of Leuven
5351:{\displaystyle p=w\rho c^{2}}
543:Discovery of cosmic microwave
194:Ultimate fate of the universe
7154:Astronomy & Astrophysics
6959:Astronomy & Astrophysics
6342:. p. 23. Archived from
6170:10.1016/0370-1573(94)00085-H
6066:with theoretical results of
1896:may be used instead of
1846:) has units of length. When
1349:) has units of length. When
726:(or otherwise, contracting)
7598:Relativistic Doppler effect
7184:10.1051/0004-6361/202039840
6989:10.1051/0004-6361/201936602
6904:10.1016/j.jheap.2022.04.002
6031:Unsolved problem in physics
5693:first law of thermodynamics
5090:first law of thermodynamics
4817:is well approximated by an
3817:Gravitational time dilation
2239:{\displaystyle {\sqrt {k}}}
1401:coordinates the coordinate
758:– are variously grouped as
311:Black Hole Initiative (BHI)
8391:
8069:In computational physics:
7593:Relativity of simultaneity
7321:North, John David (1990).
6068:Ehlers–Geren–Sachs theorem
6022:
5121:{\displaystyle {\dot {a}}}
4441:Einstein's field equations
4364:
3937:Mathisson–Papapetrou–Dixon
3778:Pseudo-Riemannian manifold
3432:and the Ricci scalar is
2737:and the Ricci scalar is
1830:Alternatively, as before,
1389:Hyperspherical coordinates
764:Friedmann–Robertson–Walker
74:Chronology of the universe
8251:
7906:Lense–Thirring precession
7488:Doubly special relativity
7211:The Astrophysical Journal
6454:10.1142/S021773231550100x
6392:10.1007/s10773-006-9123-2
6286:Carroll, Sean M. (2019).
5728:The Soviet mathematician
4425:{\displaystyle \rho (t),}
2266:= 0 one may write simply
1285:Schwarzschild coordinates
714:. The metric describes a
167:Expansion of the universe
7766:Post-Newtonian formalism
7756:Einstein field equations
7692:Mathematical formulation
7516:Hyperbolic orthogonality
7342:Harrison, E. R. (1967).
7296:10.1088/1361-6382/ac1a81
7242:10.3847/2041-8213/abdd40
7057:10.1088/1361-6382/ac1a81
6569:Zeitschrift für Physik A
6523:Zeitschrift für Physik A
6424:Modern Physics Letters A
6311:Wald, Robert M. (1984).
6261:Wald, Robert M. (1984).
5437:Newtonian interpretation
5085:for the first equation.
3942:Hamilton–Jacobi–Einstein
3922:Einstein field equations
3745:Mathematical formulation
2363:This can be extended to
1761:has units of length and
1236:has units of length and
708:Einstein field equations
331:Planck space observatory
117:Gravitational wave (GWB)
7477:Galilean transformation
7468:Principle of relativity
7385:D'Inverno, Ray (1992).
7176:2021A&A...653A...9S
6981:2020A&A...636A..15M
6853:10.1112/plms/s2-42.1.90
6505:10.1093/qmath/os-5.1.73
5967:is the speed of light,
5083:constant of integration
184:Inhomogeneous cosmology
18:Robertson–Walker metric
7562:Lorentz transformation
7369:10.1093/mnras/137.1.69
6639:10.1093/mnras/91.5.483
6092:
6038:cosmological principle
6005:
5981:
5961:
5938:
5875:
5783:Arthur Geoffrey Walker
5744:Zeitschrift für Physik
5735:Zeitschrift für Physik
5678:
5559:
5420:
5352:
5300:
5247:
5204:
5122:
5075:
5052:
4926:
4795:
4649:
4516:energy–momentum tensor
4504:
4426:
4394:
3812:Gravitational redshift
3705:
3612:
3423:
3256:
3111:
2955:
2885:
2728:
2554:
2502:
2452:
2406:
2354:
2240:
2209:
2126:
1975:
1817:
1788:. Where appropriate,
1741:
1531:
1501:
1316:
1287:). Where appropriate,
1213:
995:
956:
931:
756:Arthur Geoffrey Walker
734:, but not necessarily
8030:Weyl−Lewis−Papapetrou
7771:Raychaudhuri equation
7710:Equivalence principle
7087:Hawking, Stephen W.;
6791:Astrophysical Journal
6750:Astrophysical Journal
6711:Astrophysical Journal
6093:
6091:{\displaystyle H_{0}}
6025:Shape of the universe
6006:
6004:{\displaystyle \rho }
5982:
5962:
5939:
5876:
5716:, one cannot neglect
5707:cosmological constant
5679:
5560:
5421:
5353:
5301:
5258:cosmological constant
5248:
5205:
5154:cosmological constant
5148:Cosmological constant
5140:, on the other hand,
5138:cosmological constant
5123:
5076:
5053:
4927:
4796:
4650:
4505:
4427:
4395:
4100:Weyl−Lewis−Papapetrou
4055:Kerr–Newman–de Sitter
3875:Einstein–Rosen bridge
3807:Gravitational lensing
3763:Equivalence principle
3706:
3613:
3424:
3257:
3112:
2956:
2895:Spherical coordinates
2886:
2729:
2555:
2553:{\displaystyle (k=0)}
2524:Cartesian coordinates
2503:
2453:
2407:
2355:
2258:Cartesian coordinates
2241:
2210:
2127:
1955:
1818:
1742:
1532:
1502:
1317:
1214:
996:
957:
932:
275:Large-scale structure
253:Shape of the universe
8071:Numerical relativity
7912:pulsar timing arrays
6565:Friedmann, Alexander
6519:Friedmann, Alexander
6075:
5995:
5971:
5951:
5891:
5835:
5742:, who, on behalf of
5570:
5448:
5379:
5323:
5267:
5215:
5163:
5103:
5065:
4937:
4848:
4660:
4525:
4446:
4404:
4393:{\displaystyle a(t)}
4375:
4030:Einstein–Rosen waves
3756:Fundamental concepts
3645:
3439:
3267:
3122:
2966:
2906:
2744:
2571:
2532:
2464:
2417:
2377:
2273:
2226:
2142:
1930:
1800:
1544:
1514:
1412:
1399:curvature-normalized
1299:
1032:
978:
944:
821:
587:Astronomy portal
545:background radiation
522:List of cosmologists
7963:Friedmann equations
7857:Hulse–Taylor binary
7819:Gravitational waves
7715:Riemannian geometry
7541:Proper acceleration
7526:Maxwell's equations
7472:Galilean relativity
7360:1967MNRAS.137...69H
7288:2021CQGra..38r4001K
7233:2021ApJ...908L..51S
7128:1995ApJ...443....1S
7089:Ellis, George F. R.
7049:2021CQGra..38r4001K
6965:(April 2020): A15.
6932:Scientific American
6896:2022JHEAp..34...49A
6845:1937PLMS...42...90W
6804:1936ApJ....83..257R
6763:1936ApJ....83..187R
6724:1935ApJ....82..284R
6693:1933ASSB...53...51L
6664:1927ASSB...47...49L
6630:1931MNRAS..91..483L
6581:1924ZPhy...21..326F
6535:1922ZPhy...10..377F
6497:1934QJMat...5...73M
6446:2015MPLA...3050100R
6384:2006IJTP...45.1152R
6211:1999ASIC..541....1E
6162:1995PhR...254..135L
5824:, a long-abandoned
5822:Einstein's universe
5818:radius of curvature
5779:Howard P. Robertson
5730:Alexander Friedmann
4815:observable universe
4512:Friedmann equations
4367:Friedmann equations
3984:Kaluza–Klein theory
3870:Minkowski spacetime
3822:Gravitational waves
1873:). Note that when
1863:radius of curvature
1366:radius of curvature
1001:does not depend on
752:Howard P. Robertson
744:Alexander Friedmann
287:Structure formation
179:Friedmann equations
69:Age of the universe
33:Part of a series on
8370:Physical cosmology
8012:Reissner–Nordström
7930:Brans–Dicke theory
7761:Linearized gravity
7588:Length contraction
7506:Frame of reference
7483:Special relativity
7085:See pp. 351ff. in
6589:10.1007/BF01328280
6543:10.1007/BF01332580
6313:General relativity
6263:General relativity
6088:
6001:
5977:
5957:
5934:
5871:
5674:
5555:
5416:
5363:general invariance
5348:
5296:
5243:
5200:
5134:general relativity
5118:
5071:
5048:
4922:
4791:
4645:
4500:
4422:
4390:
4313:Physics portal
4085:Oppenheimer–Snyder
4025:Reissner–Nordström
3917:Linearized gravity
3865:Spacetime diagrams
3768:Special relativity
3701:
3630:General relativity
3608:
3419:
3252:
3107:
2951:
2881:
2724:
2550:
2498:
2448:
2402:
2350:
2236:
2205:
2122:
1813:
1775:Gaussian curvature
1737:
1732:
1527:
1497:
1312:
1250:Gaussian curvature
1209:
991:
952:
927:
780:Friedmann–Lemaître
712:general relativity
326:Dark Energy Survey
270:Large quasar group
39:Physical cosmology
8265:
8264:
8079:
8078:
8058:Ozsváth–Schücking
7664:
7663:
7646:Minkowski diagram
7603:Thomas precession
7546:Relativistic mass
7400:978-0-19-859686-8
7334:978-0-486-66517-7
7104:978-0-521-09906-6
6677:Lemaître, Georges
6648:Lemaître, Georges
6612:Lemaître, Georges
6322:978-0-226-87032-8
6297:978-1-108-48839-6
6272:978-0-226-87032-8
6247:978-3-540-32924-4
5980:{\displaystyle G}
5960:{\displaystyle c}
5929:
5901:
5862:
5847:
5668:
5640:
5597:
5585:
5552:
5538:
5501:
5473:
5411:
5238:
5198:
5144:of the universe.
5115:
5094:adiabatic process
5074:{\displaystyle k}
5046:
5016:
4983:
4955:
4950:
4915:
4887:
4882:
4860:
4819:almost FLRW model
4748:
4706:
4701:
4681:
4676:
4640:
4615:
4590:
4548:
4543:
4363:
4362:
3996:
3995:
3882:
3881:
3598:
3567:
3527:
3509:
3482:
3463:
3364:
3336:
3219:
3191:
3105:
3053:
3025:
2946:
2941:
2871:
2831:
2813:
2786:
2712:
2693:
2611:
2606:
2234:
2197:
2114:
2082:
2051:
1910:analytic function
1825:comoving distance
1711:
1672:
1612:
1583:
1537:is as before and
1324:comoving distance
1134:
1095:
1013:), known as the "
623:
622:
294:
293:
136:
135:
16:(Redirected from
8382:
8342:
8341:
8340:
8330:
8329:
8328:
8318:
8317:
8316:
8306:
8305:
8294:
8293:
8292:
8282:
8281:
8273:
8257:
8256:
8040:van Stockum dust
7812:Two-body problem
7730:Mach's principle
7677:
7618:Terrell rotation
7458:
7436:
7429:
7422:
7413:
7404:
7392:
7381:
7371:
7338:
7308:
7307:
7281:
7261:
7255:
7254:
7244:
7226:
7202:
7196:
7195:
7169:
7148:
7142:
7140:
7139:
7107:
7083:
7077:
7076:
7042:
7022:
7016:
7015:
7013:
7011:
6974:
6950:
6944:
6943:
6941:
6939:
6922:
6916:
6915:
6889:
6869:
6856:
6855:
6823:
6817:
6816:
6815:
6786:Robertson, H. P.
6782:
6776:
6775:
6774:
6745:Robertson, H. P.
6741:
6735:
6734:
6706:Robertson, H. P.
6702:
6696:
6695:
6673:
6667:
6666:
6642:
6641:
6608:
6602:
6600:
6561:
6555:
6554:
6515:
6509:
6508:
6480:
6474:
6473:
6439:
6418:
6412:
6411:
6377:
6368:(6): 1152–1157.
6357:
6351:
6350:
6349:on Jan 11, 2020.
6348:
6341:
6333:
6327:
6326:
6308:
6302:
6301:
6283:
6277:
6276:
6258:
6252:
6251:
6231:
6225:
6224:
6204:
6188:
6182:
6181:
6155:
6133:
6127:
6120:
6105:
6103:
6097:
6095:
6094:
6089:
6087:
6086:
6056:Lambda-CDM model
6032:
6010:
6008:
6007:
6002:
5986:
5984:
5983:
5978:
5966:
5964:
5963:
5958:
5943:
5941:
5940:
5935:
5930:
5916:
5914:
5903:
5902:
5899:
5880:
5878:
5877:
5872:
5864:
5863:
5855:
5849:
5848:
5840:
5781:from the US and
5767:Arthur Eddington
5751:Georges Lemaître
5724:Name and history
5683:
5681:
5680:
5675:
5669:
5664:
5663:
5662:
5649:
5641:
5639:
5631:
5627:
5626:
5617:
5616:
5603:
5598:
5593:
5592:
5587:
5586:
5578:
5574:
5564:
5562:
5561:
5556:
5553:
5551:
5550:
5541:
5540:
5539:
5531:
5525:
5524:
5511:
5503:
5502:
5494:
5491:
5490:
5475:
5474:
5466:
5463:
5462:
5425:
5423:
5422:
5417:
5412:
5407:
5406:
5405:
5392:
5357:
5355:
5354:
5349:
5347:
5346:
5305:
5303:
5302:
5297:
5291:
5290:
5252:
5250:
5249:
5244:
5239:
5231:
5209:
5207:
5206:
5201:
5199:
5197:
5196:
5195:
5179:
5127:
5125:
5124:
5119:
5117:
5116:
5108:
5080:
5078:
5077:
5072:
5057:
5055:
5054:
5049:
5047:
5042:
5041:
5040:
5027:
5022:
5018:
5017:
5015:
5014:
5005:
4997:
4984:
4979:
4978:
4977:
4964:
4956:
4951:
4943:
4941:
4931:
4929:
4928:
4923:
4921:
4917:
4916:
4914:
4913:
4901:
4888:
4883:
4875:
4873:
4862:
4861:
4853:
4800:
4798:
4797:
4792:
4784:
4783:
4765:
4764:
4749:
4747:
4746:
4737:
4736:
4735:
4722:
4717:
4716:
4711:
4707:
4702:
4694:
4692:
4682:
4677:
4669:
4667:
4654:
4652:
4651:
4646:
4641:
4636:
4635:
4634:
4621:
4616:
4611:
4610:
4609:
4596:
4591:
4589:
4588:
4579:
4578:
4577:
4564:
4559:
4558:
4553:
4549:
4544:
4536:
4534:
4509:
4507:
4506:
4501:
4499:
4498:
4480:
4479:
4461:
4460:
4431:
4429:
4428:
4423:
4399:
4397:
4396:
4391:
4355:
4348:
4341:
4328:
4323:
4322:
4315:
4311:
4310:
4095:van Stockum dust
4080:Robertson–Walker
3906:
3796:
3710:
3708:
3707:
3702:
3700:
3699:
3687:
3679:
3678:
3660:
3659:
3640:
3626:
3617:
3615:
3614:
3609:
3604:
3600:
3599:
3597:
3587:
3586:
3573:
3568:
3566:
3556:
3555:
3545:
3535:
3534:
3529:
3528:
3520:
3515:
3510:
3508:
3494:
3484:
3483:
3475:
3471:
3464:
3462:
3461:
3449:
3428:
3426:
3425:
3420:
3406:
3405:
3372:
3371:
3366:
3365:
3357:
3338:
3337:
3329:
3311:
3310:
3295:
3294:
3282:
3281:
3261:
3259:
3258:
3253:
3227:
3226:
3221:
3220:
3212:
3193:
3192:
3184:
3166:
3165:
3150:
3149:
3137:
3136:
3116:
3114:
3113:
3108:
3106:
3104:
3103:
3102:
3083:
3061:
3060:
3055:
3054:
3046:
3027:
3026:
3018:
3000:
2999:
2986:
2981:
2980:
2960:
2958:
2957:
2952:
2947:
2942:
2934:
2932:
2921:
2920:
2890:
2888:
2887:
2882:
2877:
2873:
2872:
2870:
2860:
2859:
2849:
2839:
2838:
2833:
2832:
2824:
2819:
2814:
2812:
2798:
2788:
2787:
2779:
2775:
2768:
2767:
2733:
2731:
2730:
2725:
2720:
2719:
2714:
2713:
2705:
2695:
2694:
2686:
2677:
2676:
2661:
2660:
2645:
2644:
2629:
2628:
2612:
2607:
2599:
2597:
2586:
2585:
2559:
2557:
2556:
2551:
2507:
2505:
2504:
2499:
2457:
2455:
2454:
2449:
2411:
2409:
2408:
2403:
2369:
2359:
2357:
2356:
2351:
2346:
2345:
2336:
2328:
2327:
2318:
2310:
2309:
2300:
2292:
2291:
2286:
2280:
2245:
2243:
2242:
2237:
2235:
2230:
2214:
2212:
2211:
2206:
2198:
2193:
2184:
2154:
2153:
2131:
2129:
2128:
2123:
2115:
2110:
2109:
2108:
2099:
2098:
2088:
2083:
2078:
2077:
2076:
2063:
2052:
2050:
2027:
2026:
2025:
2007:
2006:
1997:
1996:
1977:
1974:
1969:
1942:
1941:
1879:
1852:
1838:is unitless and
1822:
1820:
1819:
1814:
1812:
1807:
1787:
1769:) is unitless.
1746:
1744:
1743:
1738:
1736:
1735:
1712:
1710:
1702:
1697:
1683:
1682:
1673:
1671:
1663:
1658:
1613:
1608:
1594:
1593:
1584:
1579:
1556:
1555:
1536:
1534:
1533:
1528:
1526:
1521:
1506:
1504:
1503:
1498:
1496:
1495:
1490:
1484:
1478:
1477:
1462:
1461:
1449:
1448:
1439:
1431:
1430:
1425:
1419:
1355:
1341:is unitless and
1336:
1321:
1319:
1318:
1313:
1311:
1306:
1278:
1262:
1218:
1216:
1215:
1210:
1205:
1204:
1195:
1183:
1182:
1170:
1169:
1160:
1152:
1151:
1146:
1140:
1135:
1132:
1126:
1125:
1120:
1114:
1109:
1108:
1096:
1094:
1093:
1092:
1073:
1072:
1071:
1062:
1056:
1051:
1050:
1045:
1039:
1000:
998:
997:
992:
990:
985:
972:hyperbolic space
964:elliptical space
961:
959:
958:
953:
951:
936:
934:
933:
928:
923:
922:
917:
911:
906:
905:
900:
882:
881:
872:
867:
866:
851:
850:
841:
836:
835:
796:Lambda-CDM model
772:Robertson–Walker
748:Georges Lemaître
736:simply connected
697:
696:
693:
689:
688:
685:
682:
679:
676:
673:
670:
667:
663:
662:
659:
656:
653:
650:
647:
644:
641:
615:
608:
601:
585:
584:
583:
572:
571:
265:Galaxy formation
225:Lambda-CDM model
214:
206:Components
88:
49:
30:
21:
8390:
8389:
8385:
8384:
8383:
8381:
8380:
8379:
8350:
8349:
8348:
8338:
8336:
8326:
8324:
8314:
8312:
8300:
8290:
8288:
8276:
8268:
8266:
8261:
8247:
8075:
7979:BKL singularity
7969:Lemaître–Tolman
7944:
7940:Quantum gravity
7922:
7916:
7902:geodetic effect
7876:(together with
7846:LISA Pathfinder
7785:
7734:
7720:Penrose diagram
7702:
7696:
7671:
7660:
7656:Minkowski space
7622:
7566:
7550:
7498:
7492:
7452:
7445:
7440:
7401:
7384:
7341:
7335:
7320:
7317:
7315:Further reading
7312:
7311:
7263:
7262:
7258:
7204:
7203:
7199:
7151:
7149:
7145:
7109:
7105:
7086:
7084:
7080:
7024:
7023:
7019:
7009:
7007:
6952:
6951:
6947:
6937:
6935:
6924:
6923:
6919:
6871:
6870:
6859:
6825:
6824:
6820:
6784:
6783:
6779:
6743:
6742:
6738:
6704:
6703:
6699:
6675:
6674:
6670:
6646:
6644:translated from
6610:
6609:
6605:
6563:
6562:
6558:
6517:
6516:
6512:
6482:
6481:
6477:
6430:(20): 1550100.
6421:
6419:
6415:
6359:
6358:
6354:
6346:
6339:
6335:
6334:
6330:
6323:
6310:
6309:
6305:
6298:
6285:
6284:
6280:
6273:
6260:
6259:
6255:
6248:
6233:
6232:
6228:
6221:
6190:
6189:
6185:
6139:Physics Reports
6135:
6134:
6130:
6121:
6117:
6112:
6104:1 km/s/Mpc
6101:
6099:
6078:
6073:
6072:
6052:
6051:
6046:
6034:
6030:
6027:
6021:
5993:
5992:
5969:
5968:
5949:
5948:
5894:
5889:
5888:
5833:
5832:
5811:
5740:Albert Einstein
5726:
5654:
5650:
5632:
5618:
5608:
5604:
5575:
5568:
5567:
5542:
5516:
5512:
5482:
5454:
5446:
5445:
5439:
5397:
5393:
5377:
5376:
5372:that satisfies
5361:would not have
5338:
5321:
5320:
5282:
5265:
5264:
5256:Therefore, the
5213:
5212:
5187:
5183:
5161:
5160:
5150:
5101:
5100:
5063:
5062:
5032:
5028:
5006:
4998:
4989:
4985:
4969:
4965:
4935:
4934:
4905:
4893:
4889:
4846:
4845:
4839:
4775:
4756:
4738:
4727:
4723:
4687:
4686:
4658:
4657:
4626:
4622:
4601:
4597:
4580:
4569:
4565:
4529:
4528:
4523:
4522:
4487:
4468:
4449:
4444:
4443:
4402:
4401:
4373:
4372:
4369:
4359:
4318:
4305:
4304:
4297:
4296:
4120:
4119:
4110:
4109:
4065:Lemaître–Tolman
4010:
4009:
3998:
3997:
3989:Quantum gravity
3976:Advanced theory
3903:
3902:
3901:
3884:
3883:
3832:Geodetic effect
3793:
3792:
3783:
3782:
3758:
3757:
3741:
3711:
3688:
3667:
3648:
3643:
3642:
3624:
3578:
3577:
3547:
3546:
3517:
3516:
3495:
3472:
3469:
3465:
3453:
3437:
3436:
3397:
3354:
3299:
3286:
3270:
3265:
3264:
3209:
3154:
3141:
3125:
3120:
3119:
3094:
3084:
3043:
2988:
2987:
2969:
2964:
2963:
2909:
2904:
2903:
2897:
2851:
2850:
2821:
2820:
2799:
2776:
2773:
2769:
2756:
2742:
2741:
2702:
2665:
2649:
2633:
2617:
2574:
2569:
2568:
2530:
2529:
2526:
2521:
2462:
2461:
2415:
2414:
2375:
2374:
2364:
2337:
2319:
2301:
2281:
2271:
2270:
2260:
2224:
2223:
2145:
2140:
2139:
2100:
2090:
2089:
2068:
2064:
2028:
2008:
1998:
1988:
1978:
1933:
1928:
1927:
1874:
1847:
1798:
1797:
1778:
1731:
1730:
1719:
1656:
1653:
1652:
1641:
1632:
1631:
1620:
1577:
1570:
1547:
1542:
1541:
1512:
1511:
1485:
1469:
1453:
1440:
1420:
1410:
1409:
1391:
1350:
1334:
1329:Alternatively,
1297:
1296:
1276:
1253:
1244:) is unitless.
1196:
1174:
1161:
1141:
1115:
1100:
1084:
1074:
1063:
1057:
1040:
1030:
1029:
1023:
976:
975:
968:Euclidean space
942:
941:
912:
886:
873:
858:
842:
827:
819:
818:
804:
691:
664:
638:
634:
619:
581:
579:
561:
560:
547:
544:
537:
535:Subject history
527:
526:
518:
363:
355:
354:
351:
348:
306:
296:
295:
258:Galaxy filament
211:
199:
198:
150:
145:Expansion
138:
137:
122:Microwave (CMB)
101:Nucleosynthesis
85:
28:
23:
22:
15:
12:
11:
5:
8388:
8386:
8378:
8377:
8375:Metric tensors
8372:
8367:
8362:
8352:
8351:
8347:
8346:
8334:
8322:
8310:
8298:
8286:
8263:
8262:
8252:
8249:
8248:
8246:
8245:
8238:
8233:
8228:
8223:
8218:
8213:
8208:
8203:
8198:
8193:
8188:
8183:
8178:
8173:
8168:
8166:Choquet-Bruhat
8163:
8158:
8153:
8148:
8143:
8138:
8133:
8128:
8123:
8118:
8113:
8108:
8103:
8098:
8093:
8087:
8085:
8081:
8080:
8077:
8076:
8074:
8073:
8066:
8065:
8060:
8055:
8048:
8047:
8042:
8037:
8032:
8027:
8018:Axisymmetric:
8015:
8014:
8009:
8003:
7992:
7991:
7986:
7981:
7976:
7971:
7966:
7957:Cosmological:
7954:
7952:
7946:
7945:
7943:
7942:
7937:
7932:
7926:
7924:
7918:
7917:
7915:
7914:
7909:
7898:frame-dragging
7895:
7890:
7885:
7882:Einstein rings
7878:Einstein cross
7871:
7860:
7859:
7854:
7848:
7843:
7838:
7825:
7815:
7814:
7809:
7804:
7799:
7793:
7791:
7787:
7786:
7784:
7783:
7781:Ernst equation
7778:
7773:
7768:
7763:
7758:
7753:
7751:BSSN formalism
7748:
7742:
7740:
7736:
7735:
7733:
7732:
7727:
7722:
7717:
7712:
7706:
7704:
7698:
7697:
7695:
7694:
7689:
7683:
7681:
7674:
7666:
7665:
7662:
7661:
7659:
7658:
7653:
7648:
7643:
7638:
7632:
7630:
7624:
7623:
7621:
7620:
7615:
7610:
7608:Ladder paradox
7605:
7600:
7595:
7590:
7585:
7580:
7574:
7572:
7568:
7567:
7565:
7564:
7558:
7556:
7552:
7551:
7549:
7548:
7543:
7538:
7533:
7528:
7523:
7518:
7513:
7511:Speed of light
7508:
7502:
7500:
7494:
7493:
7491:
7490:
7485:
7480:
7474:
7464:
7462:
7455:
7447:
7446:
7441:
7439:
7438:
7431:
7424:
7416:
7410:
7409:
7399:
7382:
7339:
7333:
7316:
7313:
7310:
7309:
7272:(18): 184001.
7256:
7197:
7143:
7137:10.1086/175496
7103:
7078:
7033:(18): 184001.
7017:
6945:
6917:
6857:
6818:
6813:10.1086/143726
6777:
6772:10.1086/143716
6736:
6732:10.1086/143681
6697:
6668:
6624:(5): 483–490,
6603:
6575:(1): 326–332.
6556:
6529:(1): 377–386.
6510:
6475:
6413:
6352:
6328:
6321:
6303:
6296:
6278:
6271:
6253:
6246:
6226:
6220:978-0792359463
6219:
6183:
6146:(3): 135–214.
6128:
6114:
6113:
6111:
6108:
6085:
6081:
6047:
6035:
6029:
6020:
6019:Current status
6017:
6000:
5976:
5956:
5945:
5944:
5933:
5928:
5925:
5922:
5919:
5913:
5909:
5906:
5897:
5882:
5881:
5870:
5867:
5861:
5858:
5852:
5846:
5843:
5810:
5807:
5725:
5722:
5685:
5684:
5673:
5667:
5661:
5657:
5653:
5647:
5644:
5638:
5635:
5630:
5625:
5621:
5615:
5611:
5607:
5601:
5596:
5591:
5584:
5581:
5565:
5549:
5545:
5537:
5534:
5528:
5523:
5519:
5515:
5509:
5506:
5500:
5497:
5489:
5485:
5481:
5478:
5472:
5469:
5461:
5457:
5453:
5438:
5435:
5427:
5426:
5415:
5410:
5404:
5400:
5396:
5390:
5387:
5384:
5359:
5358:
5345:
5341:
5337:
5334:
5331:
5328:
5307:
5306:
5295:
5289:
5285:
5281:
5278:
5275:
5272:
5254:
5253:
5242:
5237:
5234:
5229:
5226:
5223:
5220:
5210:
5194:
5190:
5186:
5182:
5177:
5174:
5171:
5168:
5149:
5146:
5114:
5111:
5070:
5059:
5058:
5045:
5039:
5035:
5031:
5025:
5021:
5013:
5009:
5004:
5001:
4995:
4992:
4988:
4982:
4976:
4972:
4968:
4962:
4959:
4954:
4949:
4946:
4932:
4920:
4912:
4908:
4904:
4899:
4896:
4892:
4886:
4881:
4878:
4871:
4868:
4865:
4859:
4856:
4838:
4837:Interpretation
4835:
4802:
4801:
4790:
4787:
4782:
4778:
4774:
4771:
4768:
4763:
4759:
4755:
4752:
4745:
4741:
4734:
4730:
4726:
4720:
4715:
4710:
4705:
4700:
4697:
4690:
4685:
4680:
4675:
4672:
4665:
4655:
4644:
4639:
4633:
4629:
4625:
4619:
4614:
4608:
4604:
4600:
4594:
4587:
4583:
4576:
4572:
4568:
4562:
4557:
4552:
4547:
4542:
4539:
4532:
4497:
4494:
4490:
4486:
4483:
4478:
4475:
4471:
4467:
4464:
4459:
4456:
4452:
4421:
4418:
4415:
4412:
4409:
4389:
4386:
4383:
4380:
4365:Main article:
4361:
4360:
4358:
4357:
4350:
4343:
4335:
4332:
4331:
4330:
4329:
4316:
4299:
4298:
4295:
4294:
4287:
4282:
4277:
4272:
4267:
4262:
4257:
4252:
4247:
4242:
4237:
4232:
4227:
4222:
4217:
4212:
4207:
4202:
4197:
4192:
4187:
4182:
4177:
4172:
4167:
4162:
4157:
4152:
4147:
4142:
4137:
4132:
4127:
4121:
4117:
4116:
4115:
4112:
4111:
4108:
4107:
4102:
4097:
4092:
4087:
4082:
4077:
4072:
4067:
4062:
4057:
4052:
4047:
4042:
4037:
4032:
4027:
4022:
4011:
4005:
4004:
4003:
4000:
3999:
3994:
3993:
3992:
3991:
3986:
3978:
3977:
3973:
3972:
3971:
3970:
3968:Post-Newtonian
3965:
3960:
3952:
3951:
3947:
3946:
3945:
3944:
3939:
3934:
3929:
3924:
3919:
3911:
3910:
3904:
3900:
3899:
3896:
3892:
3891:
3890:
3889:
3886:
3885:
3880:
3879:
3878:
3877:
3872:
3867:
3859:
3858:
3852:
3851:
3850:
3849:
3844:
3839:
3834:
3829:
3827:Frame-dragging
3824:
3819:
3814:
3809:
3804:
3802:Kepler problem
3794:
3790:
3789:
3788:
3785:
3784:
3781:
3780:
3775:
3770:
3765:
3759:
3755:
3754:
3753:
3750:
3749:
3748:
3747:
3742:
3740:
3739:
3734:
3729:
3723:
3721:
3713:
3712:
3698:
3695:
3691:
3686:
3682:
3677:
3674:
3670:
3666:
3663:
3658:
3655:
3651:
3641:
3633:
3632:
3623:
3620:
3619:
3618:
3607:
3603:
3596:
3593:
3590:
3585:
3581:
3576:
3571:
3565:
3562:
3559:
3554:
3550:
3544:
3541:
3538:
3533:
3526:
3523:
3513:
3507:
3504:
3501:
3498:
3493:
3490:
3487:
3481:
3478:
3468:
3460:
3456:
3452:
3447:
3444:
3430:
3429:
3418:
3415:
3412:
3409:
3404:
3400:
3396:
3393:
3390:
3387:
3384:
3381:
3378:
3375:
3370:
3363:
3360:
3353:
3350:
3347:
3344:
3341:
3335:
3332:
3326:
3323:
3320:
3317:
3314:
3309:
3306:
3302:
3298:
3293:
3289:
3285:
3280:
3277:
3273:
3262:
3251:
3248:
3245:
3242:
3239:
3236:
3233:
3230:
3225:
3218:
3215:
3208:
3205:
3202:
3199:
3196:
3190:
3187:
3181:
3178:
3175:
3172:
3169:
3164:
3161:
3157:
3153:
3148:
3144:
3140:
3135:
3132:
3128:
3117:
3101:
3097:
3093:
3090:
3087:
3082:
3079:
3076:
3073:
3070:
3067:
3064:
3059:
3052:
3049:
3042:
3039:
3036:
3033:
3030:
3024:
3021:
3015:
3012:
3009:
3006:
3003:
2998:
2995:
2991:
2984:
2979:
2976:
2972:
2961:
2950:
2945:
2940:
2937:
2930:
2927:
2924:
2919:
2916:
2912:
2896:
2893:
2892:
2891:
2880:
2876:
2869:
2866:
2863:
2858:
2854:
2848:
2845:
2842:
2837:
2830:
2827:
2817:
2811:
2808:
2805:
2802:
2797:
2794:
2791:
2785:
2782:
2772:
2766:
2763:
2759:
2755:
2752:
2749:
2735:
2734:
2723:
2718:
2711:
2708:
2701:
2698:
2692:
2689:
2683:
2680:
2675:
2672:
2668:
2664:
2659:
2656:
2652:
2648:
2643:
2640:
2636:
2632:
2627:
2624:
2620:
2615:
2610:
2605:
2602:
2595:
2592:
2589:
2584:
2581:
2577:
2549:
2546:
2543:
2540:
2537:
2525:
2522:
2520:
2517:
2509:
2508:
2497:
2493:
2490:
2487:
2484:
2481:
2478:
2475:
2472:
2469:
2459:
2446:
2443:
2440:
2437:
2434:
2431:
2428:
2425:
2422:
2412:
2401:
2397:
2394:
2391:
2388:
2385:
2382:
2361:
2360:
2349:
2344:
2340:
2335:
2331:
2326:
2322:
2317:
2313:
2308:
2304:
2299:
2295:
2290:
2285:
2279:
2259:
2256:
2233:
2216:
2215:
2204:
2201:
2196:
2191:
2188:
2183:
2180:
2177:
2174:
2169:
2166:
2163:
2160:
2157:
2152:
2148:
2133:
2132:
2121:
2118:
2113:
2107:
2103:
2097:
2093:
2086:
2081:
2075:
2071:
2067:
2061:
2058:
2055:
2049:
2046:
2043:
2040:
2037:
2034:
2031:
2024:
2021:
2018:
2015:
2011:
2005:
2001:
1995:
1991:
1987:
1984:
1981:
1973:
1968:
1965:
1962:
1958:
1954:
1951:
1948:
1945:
1940:
1936:
1902:
1901:
1828:
1811:
1806:
1748:
1747:
1734:
1729:
1726:
1723:
1720:
1718:
1715:
1709:
1705:
1701:
1695:
1692:
1689:
1686:
1681:
1678:
1670:
1666:
1662:
1655:
1654:
1651:
1648:
1645:
1642:
1640:
1637:
1634:
1633:
1630:
1627:
1624:
1621:
1619:
1616:
1611:
1606:
1603:
1600:
1597:
1592:
1589:
1582:
1576:
1575:
1573:
1568:
1565:
1562:
1559:
1554:
1550:
1525:
1520:
1508:
1507:
1494:
1489:
1483:
1476:
1472:
1468:
1465:
1460:
1456:
1452:
1447:
1443:
1438:
1434:
1429:
1424:
1418:
1395:hyperspherical
1390:
1387:
1378:
1377:
1327:
1310:
1305:
1220:
1219:
1208:
1203:
1199:
1194:
1189:
1186:
1181:
1177:
1173:
1168:
1164:
1159:
1155:
1150:
1145:
1139:
1129:
1124:
1119:
1113:
1107:
1103:
1099:
1091:
1087:
1083:
1080:
1077:
1070:
1066:
1061:
1054:
1049:
1044:
1038:
1022:
1019:
989:
984:
950:
938:
937:
926:
921:
916:
910:
904:
899:
896:
893:
890:
885:
880:
876:
871:
865:
861:
857:
854:
849:
845:
840:
834:
830:
826:
803:
802:General metric
800:
788:Standard Model
732:path-connected
704:exact solution
621:
620:
618:
617:
610:
603:
595:
592:
591:
590:
589:
577:
563:
562:
559:
558:
553:
548:
541:
538:
533:
532:
529:
528:
525:
524:
517:
516:
511:
506:
501:
496:
491:
486:
481:
476:
471:
466:
461:
456:
451:
446:
441:
436:
431:
426:
421:
416:
411:
406:
401:
396:
391:
386:
381:
376:
371:
365:
364:
361:
360:
357:
356:
353:
352:
345:
343:
338:
333:
328:
323:
318:
313:
307:
302:
301:
298:
297:
292:
291:
290:
289:
277:
272:
267:
255:
247:
246:
242:
241:
240:
239:
227:
219:
218:
212:
205:
204:
201:
200:
197:
196:
191:
186:
181:
169:
164:
151:
144:
143:
140:
139:
134:
133:
132:
131:
129:Neutrino (CNB)
119:
111:
110:
106:
105:
104:
103:
86:
84:Early universe
83:
82:
79:
78:
77:
76:
71:
66:
51:
50:
42:
41:
35:
34:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
8387:
8376:
8373:
8371:
8368:
8366:
8363:
8361:
8358:
8357:
8355:
8345:
8335:
8333:
8323:
8321:
8311:
8309:
8304:
8299:
8297:
8287:
8285:
8280:
8275:
8271:
8260:
8250:
8244:
8243:
8239:
8237:
8234:
8232:
8229:
8227:
8224:
8222:
8219:
8217:
8214:
8212:
8209:
8207:
8204:
8202:
8199:
8197:
8194:
8192:
8189:
8187:
8184:
8182:
8179:
8177:
8174:
8172:
8169:
8167:
8164:
8162:
8159:
8157:
8154:
8152:
8151:Chandrasekhar
8149:
8147:
8144:
8142:
8139:
8137:
8134:
8132:
8129:
8127:
8124:
8122:
8119:
8117:
8114:
8112:
8111:Schwarzschild
8109:
8107:
8104:
8102:
8099:
8097:
8094:
8092:
8089:
8088:
8086:
8082:
8072:
8068:
8067:
8064:
8061:
8059:
8056:
8054:
8050:
8049:
8046:
8043:
8041:
8038:
8036:
8033:
8031:
8028:
8025:
8021:
8017:
8016:
8013:
8010:
8007:
8004:
8002:
7998:
7997:Schwarzschild
7994:
7993:
7990:
7987:
7985:
7982:
7980:
7977:
7975:
7972:
7970:
7967:
7964:
7960:
7956:
7955:
7953:
7951:
7947:
7941:
7938:
7936:
7933:
7931:
7928:
7927:
7925:
7919:
7913:
7910:
7907:
7903:
7899:
7896:
7894:
7893:Shapiro delay
7891:
7889:
7886:
7883:
7879:
7875:
7872:
7869:
7865:
7862:
7861:
7858:
7855:
7852:
7849:
7847:
7844:
7842:
7839:
7837:
7836:collaboration
7833:
7829:
7826:
7824:
7820:
7817:
7816:
7813:
7810:
7808:
7805:
7803:
7802:Event horizon
7800:
7798:
7795:
7794:
7792:
7788:
7782:
7779:
7777:
7774:
7772:
7769:
7767:
7764:
7762:
7759:
7757:
7754:
7752:
7749:
7747:
7746:ADM formalism
7744:
7743:
7741:
7737:
7731:
7728:
7726:
7723:
7721:
7718:
7716:
7713:
7711:
7708:
7707:
7705:
7699:
7693:
7690:
7688:
7685:
7684:
7682:
7678:
7675:
7673:
7667:
7657:
7654:
7652:
7651:Biquaternions
7649:
7647:
7644:
7642:
7639:
7637:
7634:
7633:
7631:
7629:
7625:
7619:
7616:
7614:
7611:
7609:
7606:
7604:
7601:
7599:
7596:
7594:
7591:
7589:
7586:
7584:
7581:
7579:
7578:Time dilation
7576:
7575:
7573:
7569:
7563:
7560:
7559:
7557:
7553:
7547:
7544:
7542:
7539:
7537:
7534:
7532:
7531:Proper length
7529:
7527:
7524:
7522:
7519:
7517:
7514:
7512:
7509:
7507:
7504:
7503:
7501:
7495:
7489:
7486:
7484:
7481:
7478:
7475:
7473:
7469:
7466:
7465:
7463:
7459:
7456:
7454:
7448:
7444:
7437:
7432:
7430:
7425:
7423:
7418:
7417:
7414:
7408:
7402:
7396:
7391:
7390:
7383:
7379:
7375:
7370:
7365:
7361:
7357:
7353:
7349:
7345:
7340:
7336:
7330:
7326:
7325:
7319:
7318:
7314:
7305:
7301:
7297:
7293:
7289:
7285:
7280:
7275:
7271:
7267:
7260:
7257:
7252:
7248:
7243:
7238:
7234:
7230:
7225:
7220:
7216:
7212:
7208:
7201:
7198:
7193:
7189:
7185:
7181:
7177:
7173:
7168:
7163:
7159:
7155:
7147:
7144:
7138:
7133:
7129:
7125:
7121:
7117:
7116:Astrophys. J.
7113:
7112:Ellis, George
7106:
7100:
7096:
7095:
7090:
7082:
7079:
7074:
7070:
7066:
7062:
7058:
7054:
7050:
7046:
7041:
7036:
7032:
7028:
7021:
7018:
7006:
7002:
6998:
6994:
6990:
6986:
6982:
6978:
6973:
6968:
6964:
6960:
6956:
6949:
6946:
6934:
6933:
6928:
6921:
6918:
6913:
6909:
6905:
6901:
6897:
6893:
6888:
6883:
6879:
6875:
6868:
6866:
6864:
6862:
6858:
6854:
6850:
6846:
6842:
6839:(1): 90–127,
6838:
6834:
6833:
6828:
6827:Walker, A. G.
6822:
6819:
6814:
6809:
6805:
6801:
6797:
6793:
6792:
6787:
6781:
6778:
6773:
6768:
6764:
6760:
6756:
6752:
6751:
6746:
6740:
6737:
6733:
6729:
6725:
6721:
6717:
6713:
6712:
6707:
6701:
6698:
6694:
6690:
6686:
6682:
6678:
6672:
6669:
6665:
6661:
6657:
6653:
6649:
6645:
6640:
6635:
6631:
6627:
6623:
6619:
6618:
6613:
6607:
6604:
6598:
6594:
6590:
6586:
6582:
6578:
6574:
6571:(in German).
6570:
6566:
6560:
6557:
6552:
6548:
6544:
6540:
6536:
6532:
6528:
6524:
6520:
6514:
6511:
6506:
6502:
6498:
6494:
6490:
6486:
6479:
6476:
6471:
6467:
6463:
6459:
6455:
6451:
6447:
6443:
6438:
6433:
6429:
6425:
6417:
6414:
6409:
6405:
6401:
6397:
6393:
6389:
6385:
6381:
6376:
6375:gr-qc/0510004
6371:
6367:
6363:
6356:
6353:
6345:
6338:
6332:
6329:
6324:
6318:
6314:
6307:
6304:
6299:
6293:
6289:
6282:
6279:
6274:
6268:
6264:
6257:
6254:
6249:
6243:
6239:
6238:
6230:
6227:
6222:
6216:
6212:
6208:
6203:
6202:gr-qc/9812046
6198:
6194:
6187:
6184:
6179:
6175:
6171:
6167:
6163:
6159:
6154:
6153:gr-qc/9605010
6149:
6145:
6141:
6140:
6132:
6129:
6125:
6119:
6116:
6109:
6107:
6083:
6079:
6069:
6065:
6061:
6057:
6050:
6043:
6042:inhomogeneous
6039:
6026:
6018:
6016:
6014:
5998:
5990:
5974:
5954:
5931:
5926:
5923:
5920:
5917:
5911:
5907:
5904:
5895:
5887:
5886:
5885:
5868:
5865:
5859:
5856:
5850:
5844:
5841:
5831:
5830:
5829:
5827:
5823:
5819:
5815:
5806:
5804:
5800:
5796:
5792:
5787:
5784:
5780:
5776:
5774:
5773:
5768:
5764:
5760:
5756:
5752:
5747:
5745:
5741:
5737:
5736:
5731:
5723:
5721:
5719:
5715:
5710:
5708:
5703:
5701:
5696:
5694:
5690:
5671:
5665:
5659:
5655:
5651:
5645:
5642:
5636:
5633:
5628:
5623:
5619:
5613:
5609:
5605:
5599:
5594:
5589:
5582:
5579:
5566:
5547:
5543:
5535:
5532:
5526:
5521:
5517:
5513:
5507:
5504:
5498:
5495:
5487:
5483:
5479:
5476:
5470:
5467:
5459:
5455:
5451:
5444:
5443:
5442:
5436:
5434:
5432:
5413:
5408:
5402:
5398:
5394:
5388:
5385:
5382:
5375:
5374:
5373:
5371:
5366:
5364:
5343:
5339:
5335:
5332:
5329:
5326:
5319:
5318:
5317:
5314:
5312:
5293:
5287:
5283:
5279:
5276:
5273:
5270:
5263:
5262:
5261:
5259:
5240:
5235:
5227:
5224:
5218:
5211:
5192:
5188:
5184:
5175:
5172:
5166:
5159:
5158:
5157:
5155:
5147:
5145:
5143:
5139:
5135:
5131:
5112:
5109:
5097:
5095:
5091:
5086:
5084:
5068:
5043:
5037:
5033:
5023:
5019:
5011:
5007:
5002:
4999:
4993:
4990:
4986:
4980:
4974:
4970:
4966:
4960:
4957:
4952:
4947:
4944:
4933:
4918:
4910:
4906:
4902:
4897:
4894:
4890:
4884:
4879:
4876:
4869:
4866:
4863:
4857:
4854:
4844:
4843:
4842:
4836:
4834:
4832:
4828:
4824:
4820:
4816:
4811:
4807:
4788:
4785:
4780:
4776:
4772:
4769:
4766:
4761:
4757:
4750:
4743:
4739:
4732:
4728:
4724:
4718:
4713:
4708:
4703:
4698:
4695:
4688:
4683:
4678:
4673:
4670:
4663:
4656:
4642:
4637:
4631:
4627:
4623:
4617:
4612:
4606:
4602:
4592:
4585:
4581:
4574:
4570:
4566:
4560:
4555:
4550:
4545:
4540:
4537:
4530:
4521:
4520:
4519:
4517:
4513:
4495:
4492:
4488:
4484:
4481:
4476:
4473:
4469:
4462:
4457:
4454:
4450:
4442:
4437:
4435:
4419:
4413:
4407:
4384:
4378:
4368:
4356:
4351:
4349:
4344:
4342:
4337:
4336:
4334:
4333:
4327:
4317:
4314:
4309:
4303:
4302:
4301:
4300:
4293:
4292:
4288:
4286:
4283:
4281:
4278:
4276:
4273:
4271:
4268:
4266:
4263:
4261:
4258:
4256:
4253:
4251:
4248:
4246:
4243:
4241:
4238:
4236:
4233:
4231:
4230:Chandrasekhar
4228:
4226:
4223:
4221:
4218:
4216:
4213:
4211:
4208:
4206:
4203:
4201:
4198:
4196:
4193:
4191:
4188:
4186:
4183:
4181:
4178:
4176:
4173:
4171:
4168:
4166:
4163:
4161:
4158:
4156:
4153:
4151:
4148:
4146:
4145:Schwarzschild
4143:
4141:
4138:
4136:
4133:
4131:
4128:
4126:
4123:
4122:
4114:
4113:
4106:
4105:Hartle–Thorne
4103:
4101:
4098:
4096:
4093:
4091:
4088:
4086:
4083:
4081:
4078:
4076:
4073:
4071:
4068:
4066:
4063:
4061:
4058:
4056:
4053:
4051:
4048:
4046:
4043:
4041:
4038:
4036:
4033:
4031:
4028:
4026:
4023:
4020:
4016:
4015:Schwarzschild
4013:
4012:
4008:
4002:
4001:
3990:
3987:
3985:
3982:
3981:
3980:
3979:
3974:
3969:
3966:
3964:
3961:
3959:
3956:
3955:
3954:
3953:
3948:
3943:
3940:
3938:
3935:
3933:
3930:
3928:
3925:
3923:
3920:
3918:
3915:
3914:
3913:
3912:
3907:
3897:
3894:
3893:
3888:
3887:
3876:
3873:
3871:
3868:
3866:
3863:
3862:
3861:
3860:
3857:
3853:
3848:
3845:
3843:
3840:
3838:
3837:Event horizon
3835:
3833:
3830:
3828:
3825:
3823:
3820:
3818:
3815:
3813:
3810:
3808:
3805:
3803:
3800:
3799:
3798:
3797:
3787:
3786:
3779:
3776:
3774:
3771:
3769:
3766:
3764:
3761:
3760:
3752:
3751:
3746:
3743:
3738:
3735:
3733:
3730:
3728:
3725:
3724:
3722:
3720:
3717:
3716:
3715:
3714:
3696:
3693:
3689:
3684:
3680:
3675:
3672:
3668:
3661:
3656:
3653:
3649:
3639:
3635:
3634:
3631:
3627:
3621:
3605:
3601:
3591:
3583:
3579:
3574:
3569:
3560:
3552:
3548:
3539:
3531:
3524:
3521:
3511:
3502:
3496:
3488:
3479:
3476:
3466:
3458:
3454:
3450:
3445:
3442:
3435:
3434:
3433:
3413:
3407:
3402:
3398:
3391:
3388:
3385:
3376:
3368:
3361:
3358:
3351:
3348:
3342:
3333:
3330:
3321:
3315:
3307:
3304:
3300:
3291:
3287:
3283:
3278:
3275:
3271:
3263:
3246:
3243:
3240:
3231:
3223:
3216:
3213:
3206:
3203:
3197:
3188:
3185:
3176:
3170:
3162:
3159:
3155:
3146:
3142:
3138:
3133:
3130:
3126:
3118:
3099:
3095:
3091:
3088:
3085:
3080:
3077:
3074:
3065:
3057:
3050:
3047:
3040:
3037:
3031:
3022:
3019:
3010:
3004:
2996:
2993:
2989:
2982:
2977:
2974:
2970:
2962:
2948:
2943:
2938:
2935:
2928:
2925:
2922:
2917:
2914:
2910:
2902:
2901:
2900:
2894:
2878:
2874:
2864:
2856:
2852:
2843:
2835:
2828:
2825:
2815:
2806:
2800:
2792:
2783:
2780:
2770:
2764:
2761:
2757:
2753:
2750:
2747:
2740:
2739:
2738:
2716:
2709:
2706:
2699:
2696:
2690:
2687:
2681:
2673:
2670:
2666:
2662:
2657:
2654:
2650:
2646:
2641:
2638:
2634:
2630:
2625:
2622:
2618:
2613:
2608:
2603:
2600:
2593:
2590:
2587:
2582:
2579:
2575:
2567:
2566:
2565:
2563:
2544:
2541:
2538:
2523:
2518:
2516:
2514:
2495:
2491:
2488:
2485:
2482:
2479:
2476:
2473:
2470:
2467:
2460:
2444:
2441:
2438:
2435:
2432:
2429:
2426:
2423:
2420:
2413:
2399:
2395:
2392:
2389:
2386:
2383:
2380:
2373:
2372:
2371:
2367:
2347:
2342:
2338:
2329:
2324:
2320:
2311:
2306:
2302:
2293:
2288:
2269:
2268:
2267:
2265:
2257:
2255:
2253:
2249:
2231:
2221:
2220:sinc function
2202:
2194:
2189:
2167:
2164:
2158:
2150:
2146:
2138:
2137:
2136:
2119:
2116:
2111:
2105:
2101:
2095:
2091:
2084:
2079:
2073:
2069:
2065:
2059:
2056:
2053:
2047:
2041:
2038:
2035:
2032:
2022:
2019:
2016:
2013:
2009:
2003:
1999:
1993:
1985:
1982:
1966:
1963:
1960:
1956:
1952:
1946:
1938:
1934:
1926:
1925:
1924:
1923:
1919:
1915:
1911:
1907:
1899:
1895:
1892:. The letter
1891:
1887:
1883:
1877:
1872:
1868:
1864:
1860:
1856:
1850:
1845:
1841:
1837:
1833:
1829:
1826:
1795:
1791:
1785:
1781:
1776:
1772:
1768:
1764:
1760:
1756:
1753:
1752:
1751:
1727:
1724:
1721:
1716:
1703:
1693:
1687:
1684:
1679:
1676:
1664:
1649:
1646:
1643:
1638:
1635:
1628:
1625:
1622:
1617:
1609:
1604:
1598:
1595:
1590:
1587:
1580:
1571:
1566:
1560:
1552:
1548:
1540:
1539:
1538:
1492:
1474:
1466:
1458:
1454:
1450:
1445:
1441:
1432:
1427:
1408:
1407:
1406:
1404:
1400:
1396:
1388:
1386:
1384:
1375:
1371:
1367:
1363:
1359:
1353:
1348:
1344:
1340:
1332:
1328:
1325:
1294:
1290:
1286:
1282:
1274:
1270:
1269:circumference
1266:
1260:
1256:
1251:
1247:
1243:
1239:
1235:
1231:
1228:
1227:
1226:
1224:
1206:
1201:
1197:
1187:
1184:
1179:
1175:
1171:
1166:
1162:
1153:
1148:
1127:
1122:
1105:
1101:
1097:
1089:
1085:
1081:
1078:
1075:
1068:
1064:
1052:
1047:
1028:
1027:
1026:
1020:
1018:
1016:
1012:
1008:
1004:
973:
969:
965:
924:
919:
902:
894:
888:
883:
878:
874:
863:
859:
855:
852:
847:
843:
832:
828:
824:
817:
816:
815:
813:
809:
801:
799:
797:
793:
789:
785:
781:
777:
773:
769:
765:
761:
757:
753:
749:
745:
741:
737:
733:
729:
725:
721:
717:
713:
709:
705:
701:
695:
632:
628:
616:
611:
609:
604:
602:
597:
596:
594:
593:
588:
578:
576:
567:
566:
565:
564:
557:
554:
552:
549:
546:
540:
539:
536:
531:
530:
523:
520:
519:
515:
512:
510:
507:
505:
502:
500:
497:
495:
492:
490:
487:
485:
482:
480:
477:
475:
472:
470:
467:
465:
462:
460:
457:
455:
452:
450:
447:
445:
442:
440:
437:
435:
432:
430:
427:
425:
422:
420:
417:
415:
412:
410:
407:
405:
402:
400:
397:
395:
392:
390:
387:
385:
382:
380:
377:
375:
372:
370:
367:
366:
359:
358:
350:
344:
342:
339:
337:
334:
332:
329:
327:
324:
322:
319:
317:
314:
312:
309:
308:
305:
300:
299:
288:
285:
281:
278:
276:
273:
271:
268:
266:
263:
259:
256:
254:
251:
250:
249:
248:
243:
238:
235:
231:
228:
226:
223:
222:
221:
220:
215:
209:
203:
202:
195:
192:
190:
187:
185:
182:
180:
177:
173:
170:
168:
165:
163:
160:
156:
153:
152:
148:
142:
141:
130:
127:
123:
120:
118:
115:
114:
113:
112:
107:
102:
99:
95:
92:
91:
90:
89:
81:
80:
75:
72:
70:
67:
65:
62:
58:
55:
54:
53:
52:
48:
44:
43:
40:
36:
32:
31:
19:
8344:Solar System
8241:
7958:
7935:Kaluza–Klein
7687:Introduction
7613:Twin paradox
7406:
7388:
7354:(1): 69–79.
7351:
7347:
7323:
7269:
7265:
7259:
7214:
7210:
7200:
7157:
7153:
7146:
7119:
7115:
7093:
7081:
7030:
7026:
7020:
7008:. Retrieved
6962:
6958:
6948:
6936:. Retrieved
6930:
6920:
6887:2203.06142v1
6877:
6873:
6836:
6835:, Series 2,
6830:
6821:
6795:
6789:
6780:
6754:
6748:
6739:
6715:
6709:
6700:
6684:
6680:
6671:
6655:
6651:
6643:
6621:
6615:
6606:
6572:
6568:
6559:
6526:
6522:
6513:
6488:
6484:
6478:
6427:
6423:
6416:
6365:
6361:
6355:
6344:the original
6331:
6312:
6306:
6287:
6281:
6262:
6256:
6236:
6229:
6192:
6186:
6143:
6137:
6131:
6123:
6118:
6053:
5946:
5883:
5826:static model
5820:of space of
5813:
5812:
5802:
5798:
5794:
5790:
5788:
5777:
5770:
5763:Edwin Hubble
5758:
5748:
5743:
5733:
5727:
5714:Planck epoch
5711:
5704:
5697:
5688:
5686:
5440:
5431:quintessence
5428:
5370:scalar field
5367:
5360:
5315:
5308:
5255:
5151:
5098:
5087:
5060:
4840:
4818:
4803:
4438:
4370:
4290:
4250:Raychaudhuri
4079:
3719:Introduction
3431:
2898:
2736:
2562:Ricci tensor
2527:
2512:
2510:
2370:by defining
2365:
2362:
2263:
2261:
2251:
2247:
2217:
2134:
1922:power series
1917:
1913:
1905:
1903:
1897:
1893:
1889:
1885:
1881:
1875:
1870:
1866:
1858:
1854:
1848:
1843:
1839:
1835:
1831:
1793:
1789:
1783:
1779:
1773:is then the
1770:
1766:
1762:
1758:
1754:
1749:
1509:
1402:
1398:
1394:
1392:
1379:
1373:
1369:
1361:
1357:
1351:
1346:
1342:
1338:
1330:
1292:
1288:
1280:
1272:
1264:
1258:
1254:
1248:is then the
1245:
1241:
1237:
1233:
1229:
1222:
1221:
1024:
1015:scale factor
1010:
1006:
1002:
939:
805:
787:
783:
779:
775:
771:
767:
763:
759:
740:scale factor
702:based on an
630:
626:
624:
349:Probe (WMAP)
283:
280:Reionization
261:
233:
207:
175:
171:
158:
155:Hubble's law
146:
125:
97:
60:
8332:Outer space
8320:Spaceflight
8024:Kerr–Newman
7995:Spherical:
7864:Other tests
7807:Singularity
7739:Formulation
7701:Fundamental
7555:Formulation
7536:Proper time
7497:Fundamental
6798:: 257–271,
6757:: 187–201,
6718:: 284–301,
6337:"Cosmology"
6013:light years
5712:During the
5311:dark energy
5130:gravitation
4510:giving the
4265:van Stockum
4195:Oppenheimer
4050:Kerr–Newman
3842:Singularity
1335:{−1, 0, +1}
1133:where
808:homogeneity
716:homogeneous
304:Experiments
237:Dark matter
230:Dark energy
172:FLRW metric
109:Backgrounds
8354:Categories
8176:Zel'dovich
8084:Scientists
8063:Alcubierre
7870:of Mercury
7868:precession
7797:Black hole
7680:Background
7672:relativity
7641:World line
7636:Light cone
7461:Background
7453:relativity
7443:Relativity
7279:2105.09790
7224:2009.14826
7217:(2): L51.
7167:2010.08366
7040:2105.09790
6972:2004.03305
6880:: 49–211.
6437:1502.07033
6110:References
6023:See also:
4432:such as a
4118:Scientists
3950:Formalisms
3898:Formalisms
3847:Black hole
3773:World line
1383:elliptical
1279:(like the
790:of modern
690: ...
384:Copernicus
362:Scientists
217:Components
8296:Astronomy
8146:Robertson
8131:Friedmann
8126:Eddington
8116:de Sitter
7950:Solutions
7828:detectors
7823:astronomy
7790:Phenomena
7725:Geodesics
7628:Spacetime
7571:Phenomena
7378:0035-8711
7304:234790314
7251:222066749
7192:223953708
7073:234790314
7065:0264-9381
7005:215238834
6997:0004-6361
6938:March 24,
6912:247411131
6687:: 51–85,
6658:: 49–56,
6597:120551579
6551:125190902
6491:: 73–80.
6462:0217-7323
6408:119496918
6400:0020-7748
6178:119500217
6045:universe?
5999:ρ
5927:ρ
5921:π
5860:¨
5845:˙
5646:−
5629:ρ
5606:κ
5600:−
5583:˙
5536:˙
5505:ρ
5499:˙
5471:˙
5468:ρ
5452:−
5395:ρ
5389:−
5336:ρ
5280:ρ
5277:−
5236:κ
5233:Λ
5222:→
5185:κ
5181:Λ
5176:−
5173:ρ
5170:→
5167:ρ
5113:˙
5030:Λ
4991:ρ
4967:κ
4961:−
4948:¨
4895:ρ
4880:˙
4867:−
4858:˙
4855:ρ
4773:κ
4770:−
4754:Λ
4751:−
4699:˙
4674:¨
4643:ρ
4624:κ
4599:Λ
4593:−
4541:˙
4514:when the
4496:ν
4493:μ
4485:κ
4477:ν
4474:μ
4466:Λ
4458:ν
4455:μ
4408:ρ
4210:Robertson
4175:Friedmann
4170:Eddington
4160:Nordström
4150:de Sitter
4007:Solutions
3932:Geodesics
3927:Friedmann
3909:Equations
3895:Equations
3856:Spacetime
3791:Phenomena
3697:ν
3694:μ
3685:κ
3676:ν
3673:μ
3665:Λ
3657:ν
3654:μ
3622:Solutions
3525:˙
3480:¨
3414:θ
3408:
3362:˙
3334:¨
3305:−
3279:ϕ
3276:ϕ
3217:˙
3189:¨
3160:−
3134:θ
3131:θ
3089:−
3051:˙
3023:¨
2994:−
2939:¨
2926:−
2829:˙
2784:¨
2762:−
2710:˙
2691:¨
2671:−
2604:¨
2591:−
2519:Curvature
2492:ϕ
2489:
2483:θ
2480:
2445:ϕ
2442:
2436:θ
2433:
2396:θ
2393:
2284:Σ
2120:⋯
2117:−
2060:−
1983:−
1972:∞
1957:∑
1916:and
1861:) is the
1823:measures
1810:Σ
1688:
1677:−
1599:
1588:−
1524:Ω
1488:Ω
1423:Σ
1364:) is the
1322:measures
1309:Σ
1198:ϕ
1188:θ
1185:
1163:θ
1144:Ω
1118:Ω
1079:−
1043:Σ
988:Σ
949:Σ
915:Σ
856:−
844:τ
825:−
792:cosmology
760:Friedmann
724:expanding
720:isotropic
514:Zeldovich
414:Friedmann
389:de Sitter
316:BOOMERanG
245:Structure
210:Structure
94:Inflation
8259:Category
8136:Lemaître
8101:Einstein
8091:Poincaré
8051:Others:
8035:Taub–NUT
8001:interior
7923:theories
7921:Advanced
7888:redshift
7703:concepts
7521:Rapidity
7499:concepts
7091:(1973),
7010:24 March
6470:51948117
4806:Big Bang
4326:Category
4190:Lemaître
4155:Reissner
4140:Poincaré
4125:Einstein
4070:Taub–NUT
4035:Wormhole
4019:interior
3732:Timeline
2528:In flat
1912:of both
812:isotropy
730:that is
728:universe
575:Category
494:Suntzeff
454:Lemaître
404:Einstein
369:Aaronson
162:Redshift
64:Universe
57:Big Bang
8284:Physics
8270:Portals
8201:Hawking
8196:Penrose
8181:Novikov
8161:Wheeler
8106:Hilbert
8096:Lorentz
8053:pp-wave
7874:lensing
7670:General
7451:Special
7356:Bibcode
7284:Bibcode
7229:Bibcode
7172:Bibcode
7124:Bibcode
7122:: 1–5,
7045:Bibcode
6977:Bibcode
6892:Bibcode
6841:Bibcode
6800:Bibcode
6759:Bibcode
6720:Bibcode
6689:Bibcode
6660:Bibcode
6626:Bibcode
6577:Bibcode
6531:Bibcode
6493:Bibcode
6442:Bibcode
6380:Bibcode
6207:Bibcode
6158:Bibcode
6124:assumes
5987:is the
5816:is the
5718:quantum
4245:Hawking
4240:Penrose
4215:Bardeen
4205:Wheeler
4135:Hilbert
4130:Lorentz
4090:pp-wave
3727:History
706:of the
698:) is a
692:
499:Sunyaev
484:Schmidt
474:Penzias
469:Penrose
444:Huygens
434:Hawking
419:Galileo
8242:others
8231:Thorne
8221:Misner
8206:Taylor
8191:Geroch
8186:Ehlers
8156:Zwicky
7974:Kasner
7397:
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7331:
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7101:
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7063:
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6460:
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6319:
6294:
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6064:Planck
5991:, and
5947:where
5795:models
5791:metric
5136:. The
4324:
4291:others
4285:Thorne
4275:Newman
4255:Taylor
4235:Ehlers
4220:Walker
4185:Zwicky
4060:Kasner
2511:where
2135:or as
1908:is an
1510:where
940:where
778:), or
700:metric
573:
509:Wilson
504:Tolman
464:Newton
459:Mather
449:Kepler
439:Hubble
399:Ehlers
379:Alpher
374:Alfvén
282:
260:
232:
174:
157:
149:Future
124:
96:
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8308:Stars
8236:Weiss
8216:Bondi
8211:Hulse
8141:Milne
8045:discs
7989:Milne
7984:Gödel
7841:Virgo
7300:S2CID
7274:arXiv
7247:S2CID
7219:arXiv
7188:S2CID
7162:arXiv
7069:S2CID
7035:arXiv
7001:S2CID
6967:arXiv
6908:S2CID
6882:arXiv
6593:S2CID
6547:S2CID
6466:S2CID
6432:arXiv
6404:S2CID
6370:arXiv
6347:(PDF)
6340:(PDF)
6197:arXiv
6174:S2CID
6148:arXiv
5061:with
4260:Hulse
4200:Gödel
4180:Milne
4075:Milne
4040:Gödel
3737:Tests
2458:, and
2262:When
1786:) = 1
1261:) = 1
970:, or
489:Smoot
479:Rubin
424:Gamow
409:Ellis
394:Dicke
8171:Kerr
8121:Weyl
8020:Kerr
7880:and
7834:and
7832:LIGO
7395:ISBN
7374:ISSN
7329:ISBN
7099:ISBN
7061:ISSN
7012:2022
6993:ISSN
6940:2022
6458:ISSN
6396:ISSN
6317:ISBN
6292:ISBN
6267:ISBN
6242:ISBN
6215:ISBN
6062:and
6060:WMAP
5705:The
5386:<
5152:The
4831:WMAP
4829:and
4827:COBE
4810:ΛCDM
4270:Taub
4225:Kerr
4165:Weyl
4045:Kerr
3963:BSSN
2564:are
2222:and
1888:and
1878:= +1
1851:= ±1
1725:<
1685:sinh
1626:>
1354:= ±1
810:and
754:and
631:FLRW
625:The
429:Guth
8226:Yau
7851:GEO
7364:doi
7352:137
7292:doi
7237:doi
7215:908
7180:doi
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7132:doi
7053:doi
6985:doi
6963:636
6900:doi
6849:doi
6808:doi
6767:doi
6728:doi
6685:A53
6656:A47
6634:doi
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6539:doi
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6450:doi
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6144:254
4280:Yau
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2486:sin
2477:sin
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2390:cos
2368:≠ 0
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768:FRW
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600:v
284:·
262:·
234:·
208:·
176:·
159:·
147:·
126:·
98:·
61:·
20:)
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